The alleged tradeoff between explanatory breadth and predictive power

Auxiliary assumptions

Despite the many authorities that have espoused the tradeoff between explanatory breadth and predictive power, and the many specific cases that seem to exemplify the tradeoff, our goal is to suggest that the tradeoff provides a picture that is too simplistic and that falls well short of reality or at least well short of necessary reality. Our reasoning hinges on the importance of auxiliary assumptions for testing theories; thus, a short excursion into the nature of auxiliary assumptions is warranted.

Although psychologists often speak about making predictions from theories, this is not quite accurate because theories contain non-observational terms, whereas experimental hypotheses are at the observational level. One function of auxiliary assumptions is to bridge the gap between the non-observational terms in theories and observational terms specified by empirical hypotheses. As a famous example, Halley was able to use Newton’s theory to predict where what is now called “Halley’s Comet” would be in a particular year. But Newton’s theory never mentioned the comet. Rather, Halley had to add auxiliary assumptions about the comet (e.g., about its previous position) that, in conjunction with Newton’s theory, led to the prediction. A psychology example might involve assumptions about how to measure or manipulate attitudes to predict behaviors to test the theory of reasoned action or planned behavior. In general, theories involve non-observational terms and cannot be tested without auxiliary assumptions.

The importance of auxiliary assumptions is of particular significance in discussions about the falsifiability of theories (Duhem, 1954; Lakatos, 1976; Meehl, 1978; Quine, 1951; Trafimow, 2009). Given that predictions come from the combination of theory and auxiliary assumptions, a failed prediction might be due to the incorrectness of the theory, but it could also be due to at least one auxiliary assumption being wrong. Given that auxiliary assumptions can be blamed for failed predictions, such failures do not necessarily demonstrate that the theory is wrong. Put in more general terms, absolute falsification is impossible, though one can argue for some kind of “reasonable” falsification. An additional function of auxiliary assumptions is that they help add meaning to the non-observational terms in theories. In general, the non-observational terms in theories cannot be defined completely (e.g., the term “mass” in Newton’s famous equation that force equals the product of mass and acceleration). But the auxiliary assumptions used to submit the theories to empirical tests, while enabling the researcher to bridge the gap between the non-observational terms in theories and observational terms in empirical hypotheses, also serve to increase the clarity of meaning of the non-observational terms in theories. That auxiliary assumptions aid in meaning interpretation is made obvious by the fact that non-observational terms in theories are used in a way that is constrained by the auxiliary assumptions. But this empirical constraint also suggests meaning constraints. That is, potential meanings that are consistent with how the non-observational term in the theory is implemented through auxiliary assumptions are to be favored over potential meanings that are inconsistent with such implementation.

Back to explanatory breadth and predictive power

Given that experimental predictions are a function of the combination of theory and auxiliary assumptions, and not a function only of the theory, it follows that predictive power depends on the combination rather than on the theory alone. Put another way, predictive power depends not only on the theory, but also on the quality of the auxiliary assumptions. But if the quality of the auxiliary assumptions also matters for predictive power, then the possibility is opened that even very general theories, that have impressive explanatory breadth, might be capable of making very precise predictions provided that the researcher is sufficiently creative to make high quality auxiliary assumptions.

The example of Halley’s Comet works well here as an illustration. In 1705, Halley predicted correctly that the comet would reappear in 1758. This prediction was based on Newton’s theory and auxiliary assumptions about the comet itself, as well as gravitational perturbations due to planetary gravitational effects. Thus, Halley’s Comet provides a beautiful illustration of the ability of a theory with extraordinary explanatory breadth also being made to make an extremely precise prediction. Of course, physicists and astronomers have made many precise predictions based on Newton’s theory. As the quality of the auxiliary assumptions has increased (in part due to technological advances), so likewise has the ability of scientists to make extremely precise predictions from Newton’s theory. The example of Halley’s Comet, as well as other examples of precise predictions scientists have generated from Newton’s theory, indicate that impressive explanatory breadth need not militate against predictive power. It is possible for the two desiderata to go hand-in-hand, provided that the auxiliary assumptions employed are of sufficient quality.

Given that the foregoing physics contradict the necessity of a tradeoff between explanatory breadth and predictive power, an insistence on the tradeoff is difficult to maintain as a general characteristic of science. But perhaps the tradeoff at least can be maintained as a characteristic of psychology.

Although it is easy to come up with examples that make it appear that this is so, there is a problem with making the argument from examples. There is an important difference between arguments that “X must be so” versus arguments that “X does not have to be so.” When one supports the “must be so” argument, examples can be illustrative, but are not persuasive as evidence because the possibility remains that examples might exist which contradict the argument. Even a lack of contrary examples is not necessarily convincing because the lack fails to imply strongly that no contrary examples can exist. In contrast, when one makes the “does not have to be so” argument, a single example is instantly persuasive, provided that there is agreement that the example really applies.

With this important difference of “must be so” versus “does not have to be so” arguments in mind, and also keeping in mind that many examples in physics contradict that the tradeoff between explanatory breadth and predictive power must be so, it should be obvious that a serious argument that the tradeoff must be so, even in the relatively limited domain of psychology, is going to be difficult to maintain. And the history of psychology does have general theories that make precise and falsifiable predictions when paired with strong auxiliary assumptions. An example is behaviorism (Skinner, 1938, 1948, 1953) that has been shown to make very precise predictions under particular circumstances when strong auxiliary assumptions were available (see Malone & Cruchon, 2001 for a review). In fact, although it would be difficult to find a pure Skinnerian behaviorist today, this is not because Skinner’s behaviorism fell out of fashion but rather because it made predictions that turned out to be wrong. An obvious case involves the phenomenon of latent learning—learning that takes place without reinforcement, but that is demonstrated when the possibility of reinforcement is made available to the animal being used in the experiment. There is much additional contrary evidence too (see Chomsky, 1959 for a review).

Even the theories (psychodynamic theory and theory of reasoned action) that we cited at the beginning of this article as allegedly supporting the tradeoff between explanatory breadth and predictive power can be argued to have made predictions of sufficient precision to be falsifiable, and actually to have been falsified. Trafimow, Brown, Grace, Thompson, and Sheeran (2002) showed that Freud’s psychodynamic theory makes the empirical prediction—in conjunction with auxiliary assumptions that are well supported by the literature—that the relative influence of attitudinal versus normative effects on behavioral intentions should depend importantly on the age of the participants. And yet, when they tested the prediction, they found no such effect. Additional data ruled out the usual nuisance explanations (not enough participants, insensitive measures, and so on) as plausible excuses for the lack of an effect. Thus, contrary to the many statements that have been made that psychodynamic theory cannot make falsifiable predictions, Trafimow et al. concluded that psychodynamic theory is plain wrong. It is not unfalsifiable, but wrong!

The same is true with respect to the theory of reasoned action and its descendent, the theory of planned behavior. For example, the sufficiency assumption of this allegedly unfalsifiable theory predicts that affect should not predict unique variance in behavioral intentions above and beyond the prediction engendered by attitude, subjective norm, and perceived behavioral control. And yet, multiple articles have demonstrated that affect is both separable from theory constructs and that it accounts for unique variance in behavioral intentions (Conner & Armitage, 1998; Sniehotta, Presseau, & Araújo-Soares, 2014; Sutton, 1998; Trafimow & Sheeran, 1998; Trafimow et al., 2004). Trafimow (2009, 2015) documented multiple examples about how the theory makes falsifiable predictions that, in some cases, actually turned out to be wrong. The crucial but under-credited issue is about making high quality auxiliary assumptions.

Conclusion

So where, now, is the case for the necessity of a tradeoff between explanatory breadth and predictive power? We have seen that predictions depend, to a large extent, on the auxiliary assumptions that are combined with the theory under consideration, rather than on the theory alone. When combined with high quality auxiliary assumptions, theories with impressive explanatory breadth can, at least in principle, make sufficiently precise predictions to render some sort of reasonable falsification possible. In the case of Newton’s theory, Halley’s Comet provides a powerful example that theories that have explanatory breadth can have excellent predictive power. And as we pointed out earlier, Halley’s Comet is only one example of the predictive power of Newton’s theory; there are many others. In Newton, we have a theory that has extremely impressive explanatory breadth and extremely impressive predictive power, provided that high quality auxiliary assumptions are available. We might point out that in the famous case of the precession of the perihelion of Mercury, Newton’s theory got it wrong and, so, the data supported Einstein’s theory of relativity as being superior. Again, both of these theories have amazing explanatory breadth, but made very precise predictions when combined with high quality auxiliary assumptions. Certainly, at least in the hard sciences, the necessity of a tradeoff between explanatory breadth and predictive power cannot validly be maintained.

Nor can the necessity of the tradeoff be maintained in psychology. We have seen that although Skinner’s behaviorism has impressive explanatory breadth, the use of high quality auxiliary assumptions enabled it to make precise predictions, some of which were wrong and that falsified the theory. We also have seen that psychodynamic theory and the theory of reasoned action/planned behavior, which have impressive explanatory breadth and have been accused of being unfalsifiable, also made predictions of sufficient precision to result in falsification, at least when combined with high quality auxiliary assumptions.

Nor can the foregoing examples be overturned by examples that militate in the opposite direction. This is because those who would argue for the necessity of a tradeoff between explanatory breadth and predictive power are making a “must be so” argument, whereas we are making a “does not have to be so” argument. For the “must be so” argument to carry the day, a minimal requirement is that all examples conform, whereas for the “does not have to be so” argument to carry the day, a single contradictory example is sufficient. Between the philosophical recognition that predictions depend, in large part, on auxiliary assumptions, and the examples we presented from physics and psychology, the necessity of the tradeoff between explanatory breadth and predictive power is problematic. Philosophical arguments that depend on the necessity as an underlying assumption also are problematic.

Psychologists who are well versed in the philosophy of science are well aware of the importance of auxiliary assumptions in falsifiability discussions. However, they have somehow failed to see that auxiliary assumptions are important in other respects too. In the present article, we have demonstrated that auxiliary assumptions are also of importance in the discussion pertaining to the alleged tradeoff between explanatory breadth and predictive power. We hope and expect that philosophically oriented psychologists will continue to appreciate the general importance of auxiliary assumptions and their relevance to many additional issues in the philosophy of science.